Nature | Vol 581 | 14 May 2020 | 173a potentially useful probe of spin polarization. We observed AHE in
Ta 7 S 12 in addition to the linear ordinary Hall effect (OHE). Figure 3e
shows a nonlinear Hall effect in the proximity of zero magnetic field
and a linear OHE at high field. Although both multiband conduction
and the AHE contribute to the nonlinear Hall effect, the observed
linear OHE suggests single-carrier (hole) conduction in Ta 7 S 12 and
thus excludes multiband transport as the origin of the nonlinear Hall
effect^37 ,^38. The nonlinear Hall effect is therefore ascribed to AHE, which
arises from ferromagnetism in conductors^39. After subtracting the
linear OHE, anomalous Hall resistance of up to 0.75 Ω is observed at
1.5 K; this decreases with increasing temperature and disappears at 10 K,
which is in line with Monte Carlo simulations based on the Ising model
(Supplementary Fig. 18).
The effects of self-intercalation on the electrical properties of TMDs
were further assessed in Ta 8 Se 12 (σ = 66.7%), which forms a Kagome
lattice. It was found that the intercalation of Ta atoms and the forma-
tion of Kagome lattices stabilize the charge-density wave states. The
temperature-dependent Hall signal reveals an AHE below 15 K and
confirms ferromagnetic order in Ta 8 Se 12 (Supplementary Fig. 19, 20).
We performed DFT calculations in order to understand the origin of
the magnetization in self-intercalated Ta 7 S 12. Perfect bilayer 2Ha-stacked
Ta S 2 (Supplementary Fig. 21) possesses a non-magnetic ground state,
in which ferromagnetism can be induced by the double exchange mech-
anism^40 , triggered by the charge transfer from intercalated Ta to pristine
Ta S 2 (Fig. 3f). When the intercalated Ta adopts a 3×aa 3 superstruc-
ture, six S atoms bond with one intercalated Ta atom to form an octahe-
dral unit in the vdW gap. By contrast, each S atom is shared by three Ta
atoms in the pristine TaS 2 layer. This difference in local bonding arrange-
ment induces charge transfer from the octahedral-coordinated inter-
calated Ta atom to the prismatic-coordinated Ta atom in the TaS 2 layer
(Fig. 3f). In pristine H-phase TaS 2 , the Ta d orbitals and the S p orbitals
are well separated in terms of energy, with the states at the Fermi level
having mainly Ta dz^2 and Ta dx^2 characteristics (Supplementary Fig. 21).
In Ta 7 S 12 (σ = 33.3%), the intercalated Ta atoms introduce additional
spin-split bands across the Fermi level, and a magnetic ground state
develops (Fig. 3g, h). The magnetic moments are localized on the d orbit-
als of the intercalated Ta atom, as evidenced by the calculated interca-
lated Ta orbital-resolved spin-up and spin-down band structures in Fig. 3g100%Ta S 266.7%50%
33.3%
25%33.3% 25% Ta S 2
66.7% Ta 9 S 160%Ta Ta^7 S^12
8 S 12Ta S Ta STa:S ux ratio ≈1:10 Ta:S ux ratio ≈1:6IncreaseTa uxabTa S 2 Self-intercalatedTa 7 S 12 c MonolayerTa S 2 BilayerTa 7 S 12d fTa
ShegMonolayerTa S 2Ta S 2 Ta -TaS 2 Ta -TaS 2Ta S 2 -Ta-TaS 2Growth mechanismFormation energy (eV)Ta-rich μS (eV)–6.3 –6.0 –5.7 –5.4 –5.1 –4.8–101S-richFig. 1 | Self-intercalation in TaS 2 crystals. a, b, Schematic showing the growth
of pristine TaS 2 (a) and self-intercalated Ta 7 S 12 (b) by MBE under a low and a high
Ta-f lux environment, respectively. The lower Ta f lux produces stoichiometric
Ta S 2 , whereas a higher Ta f lux generates a self-intercalated phase. c,
Photographs of monolayer TaS 2 and bilayer Ta 7 S 12 , grown by MBE on a 2-inch
SiO 2 /Si wafer. d–f, Atomic-resolution STEM–ADF image of monolayer TaS 2
under Ta-rich conditions (d), showing an abundance of interstitial Ta atoms at
the centre of honeycomb (e) or on top of the Ta site (f). In e, f, the corresponding
atomic models are depicted on the right. g, Schematic depicting the
layer-by-layer growth of ic-2D crystals. h, Calculated formation energies of
various self-intercalated TaxSy phases with intercalation concentrations of 25%,
33.3%, 50%, 66.7% and 100%, as a function of the chemical potential of sulfur.
Scale bars: d, 2 nm; e, f, 0.5 nm.